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All Journal MATHunesa: Jurnal Ilmiah Matematika Jurnal Matematika
Elyin Fitrawati
Universitas Mataram
Mathematics

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Kontrol Optimal untuk Model SIR Campak dengan Imunisasi Menggunakan Prinsip Minimum Pontryagin Dhea Wasila Rahmi; Elyin Fitrawati; Amilia Ulul Azmi; Bulqis Nebulla Syechah; Tri Maryono Rusadi
Jurnal Matematika Vol. 16 No. 1 (2026)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Science, Udayana University Gedung UKM, Ruang UKM 8 Lt 1, Kampus Bukit Jimbaran, Badung-Bali.

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2026.v16.i01.p197

Abstract

Measles is a contagious disease that continues to affect a significant portion of the population, particularly infants and children. The disease can be prevented through immunization programs, including both basic and booster immunizations, which are part of government public health initiatives. This study aims to reduce the spread of measles while minimizing immunization costs by incorporating a control variable into the SIR (Susceptible–Infected–Recovered) model of disease transmission. The method employed is Pontryagin’s Minimum Principle to determine the optimal immunization strategy that is both effective and cost-efficient. The results indicate that the inclusion of an immunization control in the model significantly decreases the susceptible population and reduces the growth rate of the infected compartment. Furthermore, the recovered population increases more rapidly compared to the model without control. The proportion of the immunized population demonstrates that a more optimal control strategy leads to greater effectiveness in suppressing disease transmission. Therefore, the application of optimal control in the SIR model provides a valuable mathematical framework to support immunization policies for measles prevention and control.
ANALISIS TRAVELLING WAVE PADA MODEL DETERMINISTIK WABAH MONKEYPOX MENGGUNAKAN METODE CRANK- NICHOLSON Nuzla Af'idatur Robbaniyyah; Muhammad Rijal Alfian; Elyin Fitrawati
MATHunesa: Jurnal Ilmiah Matematika Vol. 14 No. 02 (2026)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v14n02.p10-21

Abstract

Health issues are still a global problem that is one of the focuses in the sustainable goals known as SDGs. Monkeypox or commonly called monkey pox is an infectious disease caused by orthopoxvirus. This disease was first discovered in 1970 and has returned to various countries since 2022 with the emergence of new, more dangerous clusters. Due to concerns about the widespread and uncontrollable spread of Covid-19, in this study, a traveling wave analysis was carried out on a deterministic model of the spread of monkeypox in humans using the Crank- Nicholson method. The diffusion equation is added to the model to form a diffusion reaction equation that will be solved to obtain a traveling wave solution. Based on the research that has been done, the results are obtained in the form of monkeypox traveling wave speed in the exposed and infected compartments around the disease-free and endemic fixed points. Based on the simulation results using the Crank-Nicholson method, it is concluded that the pattern formed describes a local outbreak that is temporary, does not develop into a large pandemic and tends to subside after spreading to a certain area.
Co-Authors Amilia Ulul Azmi Dhea Wasila Rahmi Muhammad Rijal Alfian Nuzla Af'idatur Robbaniyyah Tri Maryono Rusadi